Question

A man draws a card from pack off 52 cards ,replaces it and shuffels the pack . He continues this process until he gets a card of spade. The probability that he will fail inthe first two times isa) 9/16 b) 1/16 c) 9/64 d) None

Answer 1

A deck contain 13 spades and 39 other cards.
So the man fails for first two times and there is replacement of cards.

So in the first draw he will get one card in 39 cards.
So the probability = 39/52 =3/4

In Second draw he fails again, so the probability = 39/52 =3/4

In the third draw he succeeds, so he draw a card form 13 cards.
So the probability = 13/52 =1/4

So the probability that he fails two times = 3/4*3/4*1/4 = 9/64 (ans)